Sequential sampling for solving stochastic programs

Proceedings - Winter Simulation Conference

Volumn , Issue , 2007, Pages 421-429

  Bayraksan, Güizin ^a   Morton, David P ^b  

^a University of Arizona   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; GALLIUM ALLOYS; PROBABILITY; SOLUTIONS;

CANDIDATE SOLUTION; FEASIBLE SOLUTIONS; LIMIT POINTS; OPTIMALITY; POINT ESTIMATE; SAMPLE SIZES; SEQUENTIAL SAMPLING;

STOCHASTIC PROGRAMMING;

EID: 49749135750     PISSN: 08917736     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/WSC.2007.4419631     Document Type: Conference Paper

References (30)

1. Bayraksan, G., and D. P. Morton. 2006. Assessing solution quality in stochastic programs. Mathematical Programming 108: 495-514.
2. Bayraksan, G., and D. P. Morton. 2007. A sequential sampling procedure for stochastic programming. Technical Report, University of Arizona, Available at .
3. Chow, Y. S., and H. Robbins. 1965. On the asymptotic theory of fixed-width sequential confidence intervals for the mean. Annals of Mathematical Statistics 36: 457-62.
4. Dantzig, G. B., and P. W. Glynn. 1990. Parallel processors for planning under uncertainty. Annals of Operations Research 22: 1-21.
5. Dantzig, G. B., and G. Infanger. 1995, November. A probabilistic lower bound for two-stage stochastic programs. Technical Report SOL 95-6, Department of Operations Research, Stanford University.
6. Ermoliev, Y. 1988. Stochastic quasigradient methods. In Numerical Techniques for Stochastic Optimization, ed. Y. Ermoliev and R. Wets, 141-185. Springer-Verlag, Berlin.
7. Glynn, P. W., and W. Whitt. 1992. The asymptotic validity of sequential stopping rules for stochastic simulations. The Annals of Applied Probability 2: 180-198.
8. Higle, J. L., and S. Sen. 1991a, Statistical verification of optimally conditions for stochastic programs with recourse. Annals of Operations Research 30: 215-240.
9. Higle, J. L., and S. Sen. 1991b. Stochastic decomposition: An algorithm for two-stage linear programs with recourse. Mathematics of Operations Research 16: 650-669.
10. Higle, J. L., and S. Sen. 1996a. Duality and statistical tests of optimality for two stage stochastic programs. Mathematical Programming 75: 257-275.
11. Higle, J. L., and S. Sen. 1996b. Stochastic decomposition: A statistical method for large scale stochastic linear programming. Kluwer Academic Publishers, Dordrecht.
12. Hlávka, Z. 2000. Robust sequential methods. Ph. D. thesis, Charles University, Prague.
13. Homem-de-Mello, T. 2003. Variable-sample methods for stochastic optimization. ACM Transactions on Modeling and Computer Simulation 13: 108-133.
14. Huber, P. 1981. Robust statistics. Wiley, New York.
15. Infanger, G. 1992. Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs. Annals of Operations Research 39: 69-95.
16. Kim, S. H., and B. L. Nelson. 2001. A fully sequential procedure for indifference-zone selection in simulation. ACM TOMACS 11: 251-273.
17. Kim, S. H., and B. L. Nelson. 2006. On the asymptotic validity of fully sequential selection procedures for steady-state simulation. Operations Research 54: 475-488.
18. Law, A. M., and W. D. Kelton. 1982. Confidence intervals for steady-state simulations ii: a survey of sequential procedures. Management Science 28: 550-562.
19. Law, A. M., W. D. Kelton, and L. W. Koenig. 1981. Relative width sequential confidence intervals for the mean. Communications in Statistics B 10: 29-39.
20. Mak, W. K., D. P. Morton, and R. K. Wood. 1999. Monte Carlo bounding techniques for determining solution quality in stochastic programs. Operations Research Letters 24: 47-56.
21. Morton, D. P. 1998. Stopping rules for a class of samplingbased stochastic programming algorithms. Operations Research 46: 710-718.
22. Nadas, A. 1969. An extension of a theorem of chow and robbins on sequential confidence intervals for the mean. Annals of Mathematical Statistics 40 (2): 667-671.
23. Norkin, V. I., G. Pflug, and A. Ruszczyński. 1998. A branch and bound method for stochastic global optimization. Mathematical Programming 83: 425-450.
24. Pflug, G. 1988. Stepsize rules, stopping times and their implementations in stochastic quasigradient algorithms. In Numerical Techniques for Stochastic Optimization. Springer Verlag, Berlin.
25. Polak, E., and J. Royset. 2007. Efficient sample sizes in stochastic nonlinear programming. Journal of Computational and Applied Mathematics. Forthcoming.
26. Ruszczńiski, A. 1986. A regularized decomposition method for minimizing a sum of polyhedral functions. Mathematical Programming 35: 309-333.
27. Ruszczyński, A., and A. Świetanowski. 1997. Accelerating the regularized decomposition method for two stage stochastic linear problems. European Journal of Operational Research 101: 328-342.
28. Shapiro, A. 2003. Monte Carlo sampling methods. In Stochastic Programming, Handbooks in Operations Research and Management Science, ed. A. Ruszczyński and A. Shapiro. Elsevier, Amsterdam.
29. Shapiro, A., J. Kim, and T. Homem-de-Mello. 2002. Conditioning of convex piecewise linear stochastic programs. Mathematical Programming 94: 1-19.
30. Verweij, B., S. Ahmed, A. Kleywegt, G. Nemhauser, and A. Shapiro. 2003. The sample average approximation method applied to stochastic vehicle routing problems: A computational study. Computational and Applied Optimization 24: 289-333.